Related papers: Expressive power of linear algebra query languages
Most graph query languages are rooted in logic. By contrast, in this paper we consider graph query languages rooted in linear algebra. More specifically, we consider MATLANG, a matrix query language recently introduced, in which some basic…
We investigate the expressive power of $\mathsf{MATLANG}$, a formal language for matrix manipulation based on common matrix operations and linear algebra. The language can be extended with the operation $\mathsf{inv}$ of inverting a matrix.…
We study the expressive power of the LARA language -- a recently proposed unified model for expressing relational and linear algebra operations -- both in terms of traditional database query languages and some analytic tasks often performed…
We show that the matrix query language $\mathsf{MATLANG}$ corresponds to a natural fragment of the positive relational algebra on $K$-relations. The fragment is defined by introducing a composition operator and restricting $K$-relation…
Due to the importance of linear algebra and matrix operations in data analytics, there is significant interest in using relational query optimization and processing techniques for evaluating (sparse) linear algebra programs. In particular,…
We investigate the expressive power of regular expressions for languages of countable words and establish their expressive equivalence with logical and algebraic characterizations. Our goal is to extend the classical theory of regular…
Iterative algorithms are traditionally expressed in ACL2 using recursion. On the other hand, Common Lisp provides a construct, loop, which -- like most programming languages -- provides direct support for iteration. We describe an ACL2…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
\textsc{Lara} is a key-value algebra that aims at unifying linear and relational algebra with three types of operation abstraction. The study of \textsc{Lara}'s expressive ability reports that it can represent relational algebra and most…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
We prove a recursive identity involving formal iterated logarithms and formal iterated exponentials. These iterated logarithms and exponentials appear in a natural extension of the logarithmic formal calculus used in the study of…
One perspective on quantum algorithms is that they are classical algorithms having access to a special kind of memory with exotic properties. This perspective suggests that, even in the case of quantum algorithms, the control flow notions…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
In this paper, we present a generalized version of the matrix chain algorithm to generate efficient code for linear algebra problems, a task for which human experts often invest days or even weeks of works. The standard matrix chain problem…
Analyzing relational languages by their logical expressiveness is well understood. Something not well understood or even formalized is the vague concept of relational query patterns. What are query patterns? And how can we reason about…
A number of models of linear logic are based on or closely related to linear algebra, in the sense that morphisms are "matrices" over appropriate coefficient sets. Examples include models based on coherence spaces, finiteness spaces and…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…